Time-dependent metric for the two dimensional, non-Hermitian coupled oscillator

Abstract

We provide a time-dependent Dyson map and metric for the two dimensional harmonic oscillator with a non-Hermitian $ixy$ coupling term. This particular time-independent model exhibits spontaneously broken $\mathcal{P}\mathcal{T}$-symmetry and becomes unphysical in the broken regime, with the spectrum becoming partially complex. By introducing an explicit time-dependence into the Dyson map, we provide a time-dependent metric that renders the model consistent across the unbroken and broken regimes.

arXiv comment7 pages

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Cited by in corpus (7)

• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
• Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
• Composite quantum Coriolis forces
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Generalized gauge transformation with $PT$-symmetric non-unitary operator and classical correspondence of non-Hermitian Hamiltonian for a periodically driven system